Brownian motion with stochastic energy renewals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909645254164480 |
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| author | Santra, Ion Olsen, Kristian Stølevik |
| author_facet | Santra, Ion Olsen, Kristian Stølevik |
| contents | We investigate the impact of intermittent energy injections on a Brownian particle, modeled as stochastic renewals of its kinetic energy to a fixed value. Between renewals, the particle follows standard underdamped Langevin dynamics. For energy renewals occurring at a constant rate, we find non-Boltzmannian energy distributions that undergo a shape transition driven by the competition between the velocity relaxation timescale and the renewal timescale. In the limit of rapid renewals, the dynamics mimics one-dimensional run-and-tumble motion, while at finite renewal rates, the effective diffusion coefficient exhibits non-monotonic behavior. To quantify the system's departure from equilibrium, we derive a modified fluctuation-response relation and demonstrate the absence of a consistent effective temperature. The dissipation is characterized by deviations from equilibrium-like response, captured via the Harada-Sasa relation. Finally, we extend the analysis to non-Poissonian renewal processes and introduce a dimensionless conversion coefficient that quantifies the thermodynamic cost of diffusion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_08876 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brownian motion with stochastic energy renewals Santra, Ion Olsen, Kristian Stølevik Statistical Mechanics We investigate the impact of intermittent energy injections on a Brownian particle, modeled as stochastic renewals of its kinetic energy to a fixed value. Between renewals, the particle follows standard underdamped Langevin dynamics. For energy renewals occurring at a constant rate, we find non-Boltzmannian energy distributions that undergo a shape transition driven by the competition between the velocity relaxation timescale and the renewal timescale. In the limit of rapid renewals, the dynamics mimics one-dimensional run-and-tumble motion, while at finite renewal rates, the effective diffusion coefficient exhibits non-monotonic behavior. To quantify the system's departure from equilibrium, we derive a modified fluctuation-response relation and demonstrate the absence of a consistent effective temperature. The dissipation is characterized by deviations from equilibrium-like response, captured via the Harada-Sasa relation. Finally, we extend the analysis to non-Poissonian renewal processes and introduce a dimensionless conversion coefficient that quantifies the thermodynamic cost of diffusion. |
| title | Brownian motion with stochastic energy renewals |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2506.08876 |